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AP EAMCET202318 May 2023Morning ShiftMathematicsCircleActual

The product of the slopes of the common tangents drawn to the circles x^2+y^2+2 x-2 y-2=0 and x^2+y^2-2 x+

Options

  1. A-1
  2. B3
  3. C-8 3
  4. D1

Correct answer

D. 1

Step-by-step solution

Let S₁: x^2+y^2+2 x-2 y-2=0 aligned & C₁ (-1,1) and r₁= 1+1+2 =2 & S₂: x^2+y^2-2 x+2 y+1=0 & C₂ (1,-1) and r₂= 1+1-1 =1 aligned C ₁ P C ₂ P = r ₁ r ₂ = 2 1 C ₁ P =2 C ₂ P aligned & Now, C ₁ C ₂+ C ₂ P = C ₁ P C ₁ C ₂+ C ₂ P =2 C ₂ P & C ₁ C ₂= C ₂ P aligned So, C ₂ is mid point of C ₁ and P . aligned & -1+x₁ 2 =1 and y₁+1 2 =-1 & x₁=3, y₁=-3 aligned P ( x ₁, y ₁ )=(3,-3) Equation of line passing through P is : (y+3)=m(x-3) m x-y-3 m-3=0 ...(i) r₂= Perpendicular distance from (1,-1) to line (i) 1= | m +1-3 ~m -3 m ^

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